Nonlinear analysis of reinforced concrete cross-sections exposed to fire

A nonlinear structural analysis of cross-sections of three-dimensional reinforced concrete frames exposed to fire is presented. The analysis includes two steps: the first step is the calculation of the transient temperature field in cross-sections exposed to fire and the second step is the determination of the mechanical response due to the effect of thermal and mechanical load. A nonlinear finite-element procedure is proposed to predict the temperature field history. In this thermal analysis, the effect of moisture has been taken into account by introducing a water vapor fraction function to define the variation of enthalpy. A mechanical nonlinear analysis of the cross-sections is performed for each temperature distribution and for the applied exterior load using an algorithm of arc-length control. The mechanical and thermal properties of concrete and steel are taken according to the European Standard ENV 1991-1-2 [ENV. Eurocode 2, design of concrete structures, part 1–2: general rules—structural fire design. ENV 1992-1-2, 1995]. In order to validate the proposed thermal and mechanical models, comparisons between numerical and experimental results have been performed. The agreement found is in both cases, fairly good. In addition, a numerical example of the structural analysis of several cross-sections of a reinforced concrete waffle slab under external load and fire is shown.     

Fire resistance of axially loaded concrete filled steel tube columns

The behaviour of axially loaded square and circular concrete-filled steel tube (CFST) columns when exposed to elevated temperatures is investigated in this paper. The fire resistance of this kind of composite tubes is calculated. Comparison of the square and circular columns in the fire resistance shows that, for columns with the same steel and concrete cross-section areas, the circular column has slightly better fire resistance than the square column.     

圆钢管及钢管混凝土柱的抗火设计

分别对圆钢管、钢管混凝土、中空夹层钢管混凝土柱进行了抗火设计,并对结果进行比较分析。结果表明,在较高荷载比下柱的耐火极限不能满足实际要求,必须进行防火保护。在相同条件下,耐火极限从大到小排序为:圆钢管混凝土、中空夹层钢管混凝土、钢管柱。在一级耐火等级下,钢管混凝土柱和中空夹层钢管混凝土柱需要厚涂型钢结构防火涂料的厚度可比钢管柱分别少55%和18%以上。随着荷载比的减小或截面尺寸的增加,柱的耐火极限提高,需要的保护层厚度减小。对于钢管混凝土柱,若采用水泥砂浆保护层,其厚度是防火涂料的3倍及以上。     

Fire resistance of concrete encased steel columns under 3- and 4-side standard heating

Results from seven fire resistance experiments on concrete encased steel (CES) columns under standard fire exposure conditions are presented. The test parameters include column size, 3- and 4-side fire exposure, load intensity and load eccentricity. Data from the tests is utilized to study the effect of the aforementioned parameters on thermal and structural response of concrete encased steel columns. Test results show that CES columns have higher fire resistance under 3-side heating than that under 4-side heating. Also, load ratio and load eccentricity have a noticeable influence on the fire resistance of CES columns. In addition, spalling of the concrete decreases the fire resistance of CES columns. A comparison of measured fire resistance of CES columns with those predicted using current code provisions indicate that the current provisions may not be conservative in some situations.     

火灾下混凝土柱的温度场影响分析

利用SAFIR有限元分析软件对火灾下钢筋混凝土柱的温度场进行分析和计算,探讨高温下保护层厚度、截面周长、受火时间和截面配筋率对柱截面温度场的分布规律,为进一步认识钢筋混凝土柱的高温力学性能创造条件,并为开展火灾后钢筋混凝土柱的修复加固提供理论依据。     

Fire behaviour of concrete filled elliptical steel columns

In this work, a non-linear three-dimensional finite element model is presented in order to study the behaviour of axially loaded concrete filled elliptical hollow section (CFEHS) columns exposed to fire. This study builds on previous work carried out by the authors on concrete filled circular hollow section (CFCHS) columns both at room temperature and in fire. The numerical model is first validated at room temperature against a series of experiments on CFEHS stub columns available in the literature and subsequently extended to study the performance of slender columns at elevated temperatures. The aim of this work is to understand and represent the behaviour of axially loaded CFEHS columns in fire situations and to compare their effectiveness with that of the circular concrete filled tubular (CFT) columns. Parametric studies to explore the influence of variation in global member slenderness, load level, cross-section slenderness and section size are presented. Finally, guidance on the fire design of CFEHS columns is proposed: it is recommended to follow the guidelines of Clause 4.3.5.1 in EN 1994-1-2, but employing the flexural stiffness reduction coefficients established in the French National Annex with an equivalent EHS diameter equal to P/π, where P is the perimeter of the ellipse.     

Reliability analysis of reinforced concrete columns exposed to fire

A reliability analysis is conducted on reinforced concrete columns subjected to fire load. From an evaluation of load frequency of occurrence, load random variables are taken to be dead load, sustained live load, and fire temperature. Resistance is developed for axial capacity, with random variables taken as steel yield strength, concrete compressive strength, placement of reinforcement, and section width and height. A rational interaction model based on the Rankine approach is used to estimate column capacity as a function of fire exposure time. Various factors were considered in the analysis such as fire type, load ratio, reinforcement ratio, cover, concrete strength, load eccentricity, and other parameters. Reliability was computed from 0 to 4 h of fire exposure using Monte Carlo simulation. It was found that reliability decreased nonlinearly as a function of time, while the most significant parameters were fire type, load ratio, eccentricity, and reinforcement ratio.     

Behavior of axially-and-rotationally restrained concrete columns with ‘+’-shaped cross section and subjected to fire

Most of the previous investigations studied the structural behavior of concrete columns with ‘+’-shaped cross section at room temperature, but the behavior of such columns during a fire and the effect of boundary conditions on the mechanical properties of the heated columns have seldom been examined. In this paper, the influence of axial-and-rotational restraint on the behavior of heated concrete columns with ‘+’-shaped cross section is investigated. A self-developed finite element program RCSSCF is applied in this study. The development of column internal forces as well as deflections at the mid-height of concrete columns are discussed. Simulation results show that: (1) axial restraint can induce significant additional axial forces in concrete columns with ‘+’-shaped cross section and subjected to fire, and the additional axial forces in strongly restrained concrete columns during a fire can reach approximately 65–70% of the axial forces in columns at room temperature; (2) the fire resistance of concrete columns without rotational restraint decreases significantly with an increase of load eccentricity ratio, but that with rotational restraint is influenced lightly by load eccentricity ratio; and (3) for columns with different non-zero rotational restraint ratios, the internal axial forces, and the internal moments and deflections at the mid-height of these columns appear to follow common trends.     

Fire performance of self-consolidating concrete filled double skin steel tubular columns: Experiments

An investigation into the fire performance of self-consolidating concrete (SCC) filled double skin tubular columns (CFDST) during the standard fire test is reported. Six full size SCC filled CFDST columns were designed for the fire tests. Detail failure modes of overall specimens and each component in the columns as well as temperatures, deformation and fire endurance were presented. Fire performance of the CFDST columns were studied through analysis of the limiting temperature of the outer tube, composite action between steel and concrete and effect of a number of parameters on the fire endurance. It showed that the limiting temperature in the CFDST columns is significantly higher than that in concrete filled steel tubular (CFST) columns or critical temperature in steel structural components. Strong evidence was found to prove the existence of composite action between steel and concrete in the CFDST columns during fire exposure. Effect of a number of parameters on the fire endurance of the composite columns was identified. Investigation into the fire performance of the columns also reveals possible solutions to improve the fire resistance of CFDST members.     

钢筋混凝土T形柱的耐火极限研究

利用数值模拟程序分析了荷载比、计算长度、截面尺寸、荷载偏心率、配筋率和荷载角等参数对ISO834标准升温过程下钢筋混凝土等肢T形柱耐火极限的影响规律。针对不同荷载比、计算长度、截面尺寸、荷载偏心率、配筋率和荷载角共5400种工况进行了四周受火时等肢T形柱的高温反应分析。在此基础上,定量给出了该类构件耐火极限的实用计算方法。研究表明:(a)严格控制荷载比是提高T形柱耐火极限的有效措施。(b)随着计算长度的增加,T形柱耐火极限近似呈直线降低。(c)当荷载偏心率在0和1.0之间变化时,T形柱耐火极限随荷载偏心率的增大而减小。当荷载偏心率在1.0和2.0之间变化时,荷载偏心率改变对T形柱耐火极限影响较小。(d)荷载角对T形柱耐火极限影响较大且影响规律较为复杂。     

Fire design method for concrete filled tubular columns based on equivalent concrete core cross-section

In this work, a method for a realistic cross-sectional temperature prediction and a simplified fire design method for circular concrete filled tubular columns under axial load are presented. The generalized lack of simple proposals for computing the cross-sectional temperature field of CFT columns when their fire resistance is evaluated is evident. Even Eurocode 4 Part 1-2, which provides one of the most used fire design methods for composite columns, does not give any indications to the designers for computing the cross-sectional temperatures. Given the clear necessity of having an available method for that purpose, in this paper a set of equations for computing the temperature distribution of circular CFT columns filled with normal strength concrete is provided. First, a finite differences thermal model is presented and satisfactorily validated against experimental results for any type of concrete infill. This model consideres the gap at steel–concrete interface, the moisture content in concrete and the temperature dependent properties of both materials. Using this model, a thermal parametric analysis is executed and from the corresponding statistical analysis of the data generated, the practical expressions are derived. The second part of the paper deals with the development of a fire design method for axially loaded CFT columns based on the general rules stablished in Eurocode 4 Part 1-1 and employing the concept of room temperature equivalent concrete core cross-section. In order to propose simple equations, a multiple nonlinear regression analysis is made with the numerical results generated through a thermo-mechanical parametric analysis. Once more, predicted results are compared to experimental values giving a reasonable accuracy and slightly safe results.     

Design equation for predicting fire resistance of reinforced concrete beams

An approach for evaluating the fire resistance of reinforced concrete (RC) beams is presented in this paper. A macroscopic finite element model is applied to study the influence of various parameters on the fire resistance of RC beams. Data from parametric studies is utilized to develop a simplified expression for evaluating the fire resistance of an RC beam as a function of influencing parameters. The validity of the proposed approach is established by comparing the fire resistance predictions with those obtained from finite element studies as well as from fire resistance tests. Predictions from the proposed equation are also compared with fire resistance estimates from current codes of practice. The applicability of the approach to design situations is illustrated through a numerical example. The proposed rational approach expresses fire resistance in terms of conventional structural and material design parameters, and thus facilitates easy evaluation of fire resistance. The proposed approach provides better estimates than those from current codes of practice and thus can be used to evaluate the fire resistance of RC beams with an accuracy that is adequate for design purposes.     

Fire resistance of partially encased steel columns with restrained thermal elongation

The behaviour of composite columns made of partially encased steel sections subjected to fire has been studied numerically by several researchers. Experimental studies are scarce and there are still many phenomena to study. The influence of the axial and rotational restraint on the behaviour of these types of columns subjected to fire is still under research. This paper presents the results of a series of fire resistance tests on these types of columns with restrained thermal elongation. A new experimental set-up, specially conceived for fire resistance tests on building columns, was used for the tests. The experimental set-up was conceived so that the axial and rotational restraint of the columns would be similar to the conditions in a real building. The parameters studied were the load level, the axial and rotational restraint ratios and the slenderness of the column. The main conclusion of this work is that for low load levels the stiffness of the surrounding structure has a major influence on the behaviour of the column subjected to fire. Increasing the stiffness of the surrounding structure led to reductions in the critical times. The same behaviour was not observed for the high load levels.     

Cold-formed steel columns made with open cross-sections subjected to fire

An experimental study on the fire behaviour of cold-formed steel lipped channel (C) and built-up I (2C) slender columns with restrained thermal elongation is presented. The studied parameters were the stiffness of the surrounding structure, type of cross-section, end support conditions and initial applied load level on the columns. The results showed that increasing the stiffness of the surrounding structure and initial applied load level for the semi-rigid support conditions and both cross-sections, lead to a significant reduction of the critical temperature whereas for the pin-ended support conditions the reduction is supposed to be smaller.     

Fire performance of stiffened concrete filled double skin steel tubular columns

A major deficiency of the concrete-filled double skin steel tube (CFDST) columns in fire exposure is the inadequate steel-concrete interface bonding leading to separating concrete and steel surfaces at elevated temperatures and triggering buckling failure of the columns. To improve interface interaction as well as postpone overall buckling, it is proposed in this study to use longitudinal steel stiffeners in CFDST columns. Different patterns of stiffeners including six, four and two number of stiffeners embedded in the interior or exterior surfaces of the inner or outer tubes are considered in the analysis. A sequentially-coupled thermal-stress analysis procedure is conducted to evaluate the effects of different patterns of stiffeners on the fire performance of these columns. One of the novelties of the current study is the incorporation of the confinement effects of both inner and outer tubes on the compressive strength of concrete at elevated temperatures which gives a realistic prediction of the fire resistance behavior of the CFDST columns. From the results, it is found that among the different patterns studied, stiffeners embedded in the exterior surface of the inner tubes or interior surface of the outer tubes enhancing steel-concrete interface interaction have a determinant role in much-improving fire endurance of the columns. With increase in the load ratio fire resistance of the specimens decreases drastically. The stiffeners strength and concrete strength have minimal effect on the fire performance of the stiffened CFDST columns. The conclusions, drawn from this study, can in turn, lead to the suggestion of some guidelines for the design of CFDST columns.     

Experimental research on post-fire behaviour of reinforced concrete columns

This paper reports an experimental research into the effect of fire exposure time on the post-fire behaviour of reinforced concrete columns. Nine full-size reinforced concrete columns (45×30×300 cm) with two longitudinal reinforcement ratios (1.4% and 2.3%) were unexposed and exposed to the ISO 834 standard fire for 2 and 4 h with a constant preload. One month after cooling, the specimens were tested in axial load combined with uniaxial or biaxial bending. The test results show that the residual load-bearing capacity decreases with increase in fire exposure time. This deterioration in strength following an increase in fire exposure time can be slowed down by the strength recovery of hot rolled reinforcing bars after cooling. In addition, the reduction in residual stiffness is higher than that in ultimate load; consequently, much attention should be given to the deformation and stress redistribution of the reinforced concrete building subject to earthquakes after a fire.     

Fire resistance of composite columns with embedded I-section steel — Effects of section size and load level

This paper presents a numerical study on the fire resistance of embedded I-section composite columns designed according to EC4 Pt.1.2. The objective is to examine the effects of cross-sectional dimension and load level on column fire resistance. Four groups of columns consisting of square cross-section are chosen for study. Their cross-sectional dimensions range from 250×250 to 400×250 mm², respectively. These columns are subjected to axial compression forces and four-face uniform heating. Within each group four load levels are studied, viz., 0.2, 0.3, 0.4 and 0.5. Based on numerical analyses, it is found that under high load levels, columns with small cross-sections fail to meet the fire resistance as suggested by EC4 Pt.1.2. To validate and to prove the reliability of the numerical study, four composite columns were tested under transient heating scheme. The experimental results were validated against finite element (hereafter: FE) analyses. FE predictions of both cross-sectional temperature distribution and structural response during heating agreed reasonably well with experimental data. Column failure times are also predicted using a simple method suggested by EC4 Part 1.2. It shows that EC4 predictions agree very closely with the FE predictions.     

A numerical approach for modeling the fire induced restraint effects in reinforced concrete beams

In this paper, a model to predict the influence of fire induced restraints on the fire resistance of reinforced concrete (RC) beams is presented. The three stages, associated with the fire growth, thermal and structural analysis, for the calculation of fire resistance of the RC beams are explained. A simplified approach to account for spalling under fire conditions is incorporated into the model. The validity of the numerical model is established by comparing the predictions from the computer program with results from full-scale fire resistance tests. The program is used to conduct two case studies to investigate the influence of both the rotational and the axial restraint on the fire response of the RC beams. Through these case studies, it is shown that the restraint, both rotational and axial, has significant influence on the fire resistance of the RC beams.     

Effect of transverse reinforcement spacing on fire resistance of high strength concrete columns

The confinement effect due to the congested transverse reinforcement is a very important feature for reinforced concrete columns subjected to accidental load conditions. The influence of transverse reinforcement spacings on load bearing capacity of high strength concrete (HSC) columns at ambient temperature has been the subject of many research projects, both experimental and theoretical. However, at high temperature the results of research into this subject are scarce and do not provide unambiguous evidence as to the effect of spacing of transverse reinforcement on fire load capacity and fire resistance.The first part of this paper presents an experimental study of the influence of transverse reinforcement spacing on fire resistance of axially loaded, HSC columns with circular cross-section. The results of full-scale tests indicate that columns with spacing of ties recommended by the code provisions for design of concrete structures could suffer a premature failure as a consequence of inelastic buckling of main reinforcing bars between adjacent ties.The next part of the paper concerns the supplementary numerical analysis of tested columns. The columns were modelled in axisymmetry with embedded reinforcement. The applied material model took into account the influence of transient temperature on mechanical properties of concrete and steel. The effect of cracking, development of transient creep strains and plastic strains for concrete were also included in the analysis. The inelastic buckling of main reinforcement was modelled using average stress–strain relationships for steel in compression. The comparison of numerical simulations and experiments shows reasonable agreement. The assessment of failure modes using the numerical simulation is also presented in the paper. The results of calculations indicate that during the whole heating period high thermal gradients generated tensile stresses in the plane of cross-section of the columns. Due to this fact the confinement effect was not observed for the columns with congested spacing of transverse reinforcement.